Let $A$ be a quantum $\mathbb{P}^n$ defined by
$$
A=\mathbb{C}\langle x_1,\dots, x_{n+1}\rangle/(x_ix_j-r_{ij} x_j x_i)_{i,j}.
$$
This is known to be Noetherian. Given a homogeneous polynomial $f$ in $x_i,\dots x_{n+1}$ and assume $f$ lies in the center of $A$. Is $A/(f)$ Noetherian ring?